SAGITTA D WING DEMONSTRATOR CONFIGURATION · The aerodynamic characteristics of a diamond wing shape unmanned aerial ... Wing Half Span / Lateral Ref. Length T ... the hybrid mesh

AERODYNAMIC CHARACTERISTICS OF THE

SAGITTA DIAMOND WING DEMONSTRATOR CONFIGURATION

A. Hovelmann, C. Breitsamter

Institute of Aerodynamics and Fluid Mechanics, Technische Universitat Munchen

Boltzmannstr. 15, 85748 Garching bei Munchen, Germany

Abstract

The aerodynamic characteristics of a diamond wing shape unmanned aerial vehicle (UAV), the so called SAGITTA demon-

strator configuration, are investigated. Reynolds Averaged Navier-Stokes computations as well as wind tunnel force measure-

ments are applied to generate an aerodynamic data set for two different configurations. On the one hand, the diamond wing

UAV is considered as tail-less configuration, while on the other hand, a double vertical tail is attached to the SAGITTA demon-

strator configuration.

The results of the computed and measured aerodynamic force and moment coefficients and their corresponding

derivatives are compared to each other for both the longitudinal and the lateral motion. A good agreement between the

numerical and experimental data is observed for both regarded configurations. For the tail-less diamond wing UAV, no lateral

yaw stability is present without control surface deflection. Therefore, lateral stability is provided by vertical tails constituting

the first flight configuration within the SAGITTA demonstrator program.

NOMENCLATURE

b [m] Wing Span

CD [-] Drag Coefficient

CL [-] Lift Coefficient

CY [-] Side Force Coefficient

Cl [-] Rolling Moment Coefficient

Cm [-] Pitching Moment Coefficient

Cn [-] Yawing Moment Coefficient

cr [m] Root Chord Length

ct [m] Tip Chord Length

h [m] Flight Altitude

lV T [m] Vertical Tail Height

lμ [m] Mean Aerodynamic Chord / Longi-

tudinal Ref. Length

Ma [-] Mach Number

p∞ [N/m2] Ambient Pressure

Re [-] Reynolds Number

SRe f [m2] Reference Area

s [m] Wing Half Span / Lateral Ref. Length

T∞ [◦C] Ambient Temperature

U∞ [m/s] Freestream Velocity

α [◦] Angle of Attack

β [◦] Sideslip Angle

ϑ [◦] Roll Angle

ρ∞ [kg/m3] Ambient Density

Λ [-] Aspect Ratio

λ [-] Taper Ratio

ϕLE [◦] Sweep Angle at Leading Edge

ϕT E [◦] Sweep Angle at Trailing Edge

ψ [◦] Yaw Angle

1 INTRODUCTION

In the early stage of aircraft design, the determination of the

aerodynamic characteristics often play a major role. Within

the SAGITTA program led by EADS CASSIDIAN, these

characteristics are investigated at the Institute of Aerody-

namics and Fluid Mechanics (AER) at Technische Univer-

sitat Munchen (TUM). Launched in 2011, the SAGITTA

project focuses on the development of an unmanned aerial

vehicle (UAV) with diamond wing shape, resulting in a low-

observable wing planform. In the research program, EADS

Deutscher Luft- und Raumfahrtkongress 2012

1

DocumentID: 281220

CASSIDIAN and several partners from German universities

and research institutes work on different research topics, to

be tested on a scaled model of the diamond wing UAV, the

SAGITTA demonstrator configuration [1].

The aerodynamic characteristics of this demonstrator

UAV are determined at TUM-AER by comprehensive nu-

merical and experimental investigations, which are pre-

sented and compared in this paper. Based on the gener-

ated data set, an aerodynamic data module (ADM) is built

for the further design process of the SAGITTA demonstrator

[2]. It consists of force and moment coefficients for a wide

range of angles of attack and sideslip as well as for different

configurations. Thus, the ADM contains all relevant informa-

tion about the aerodynamic characteristics of the SAGITTA

demonstrator configuration inside its flight envelope for sub-

sequent use by all partners for their further research within

the SAGITTA demonstrator program.

Overall, diamond wing planforms have already been in-

vestigated for a long time [3]. However, compared to delta

wing configurations without trailing-edge sweep angle, a lot

less data and analyses are available in research. In recent

years, diamond wing configurations have become more im-

portant again, since the research on future UAV also fo-

cuses on this type of wing planform [4]. The presence

of a non-zero trailing-edge sweep angle at diamond wing

shapes is mainly caused by low-observability requirements

for UAV configurations. As a result of the high leading-edge

sweep angle, though, the aerodynamic characteristics of di-

amond wing planforms are quite similar to delta wing config-

urations. Aerodynamic potential and high maneuverability

known from delta wing configurations are of particular in-

terest and therefore generally maintained for diamond wing

shapes.

2 THE SAGITTA DEMONSTRATOR

CONFIGURATION

Based on preliminary studies performed by EADS CASSID-

IAN in the forefront of the research program, the wing plan-

form of the SAGITTA UAV has been defined as a diamond

wing shape featuring a 55◦ leading-edge sweep and a 25◦

trailing-edge sweep angle. The scaled SAGITTA demon-

strator configuration, which is addressed in this publication,

exhibits a wing span of b = 3.088 m and a root chord of

cr = 3 m. Due to practical reasons, the wing tip chord

has been set to ct = 0.075 m. Table 1 summarizes all

relevant geometry information about the SAGITTA demon-

strator UAV, while Figure 1 shows the wing planform of the

SAGITTA demonstrator configuration.

b [m] 3.088 ϕLE [◦] 55

cr [m] 3.000 ϕT E [◦] -25

ct [m] 0.075 λ [-] 0.025

SRe f [m2] 4.748 Λ [-] 2.010

lμ [m] 2.001

Table 1: Wing planform parameters of the SAGITTA demon-

strator configuration.

Figure 1: Wing planform of the SAGITTA demonstrator con-

figuration.

As a result of relevant constraints within the SAGITTA re-

search program, the airfoil of the demonstrator configuration

is to be of symmetric type with 12% relative thickness. Thus,

a symmetric NACA64A012 airfoil has been chosen for the

demonstrator configuration. However, the airfoil has been

modified in the inboard wing section, i.e. within the inner

20% of the wing half span. On the one hand, the airfoil has

been slightly thickened in the rear part due to installation

space requirements. On the other hand, the blunt leading

edge of the NACA airfoil has been replaced by a sharp lead-

ing edge. This geometry modification already leads at mod-

erate angles of attack to a predefined flow separation and

consequently to the formation of distinctive vortex structures

in the inboard wing section [5]. For blunt leading-edges, the

vortex formation becomes generally more complicated and

depends on several parameters [6, 7].


2

In contrast to slender delta and diamond wing shapes with

thin airfoils [8], however, the flow effects due to vortex sys-

tems are not as relevant for this non-slender diamond wing

shape with 12% relative thickness [9]. The influence of the

inboard vortex systems does not dominate the flow field

around the diamond wing shape until the angle of attack

reaches α-values near the boarder of the flight envelope

of the SAGITTA demonstrator configuration. Therefore, this

paper does not focus on vortex effects, but on the aero-

dynamic characteristics of the demonstrator UAV inside its

intended flight envelope.

Generally speaking, the SAGITTA configuration only con-

sists of its flying wing body, but due to low-observability rea-

sons it exhibits no vertical tail. Possible instabilities in both

the longitudinal and the lateral motion shall only be han-

dled by the control surfaces [10] and a thrust-vectoring sys-

tem, which is also researched within the SAGITTA program

[11]. For safety reasons, however, a double vertical tail has

been added in the preliminary design phase to the demon-

strator configuration in order to guarantee lateral stability

for the first flight tests. Based on preliminary design meth-

ods, the planform of the vertical tails has been estimated

and sized. As airfoil type, a symmetric NACA 64A008 has

been defined. Hence, the aerodynamic characteristics for

the demonstrator configuration with attached vertical tails is

also requested for the SAGITTA ADM and is regarded as

well in this paper. Figure 2 displays an isometric view of the

SAGITTA demonstrator configuration with attached vertical

tails, while the resulting planform parameters of the vertical

tail are shown in Table 2.

Figure 2: Isometric view of the SAGITTA demonstrator con-

figuration with vertical tails.

lV T [m] 0.440 ϕLE,V T [◦] 50

cr,V T [m] 0.520 ϕT E,V T [◦] 22.75

ct,V T [m] 0.180 λV T [-] 0.345

SRe f ,V T [m2] 0.154 ΛV T [-] 1.257

Table 2: Vertical tail planform parameters of the SAGITTA

demonstrator.

3 NUMERICAL METHODS

3.1 Mesh Generation

In order to investigate the aerodynamic characteristics of

the SAGITTA demonstrator configuration by computational

fluid mechanics (CFD), an appropriate mesh must be gen-

erated as input for the flow solver of choice. In the present

analysis, the hybrid mesh generator CENTAUR by Cen-

taurSoft has been used for the mesh generation process.

Based on an unstructured surface mesh consisting of trian-

gles and quadrilaterals, prismatic and hexahedral elements

are used in hybrid meshes close to the configuration so the

boundary layer can be resolved with very fine cells. Else-

where in the computational domain, which extends in the

present analysis ten wing spans in each direction around

the configuration, tetrahedral elements are used.

In order to reach a y+-value of y+ ≈ 1 on the surfaces of

the configuration, which is desired for Reynolds Averaged

Navier-Stokes (RANS) turbulence models, the resolution of

the prismatic mesh must be chosen adequately. Based on

30 prism layers and a stretching factor of 1.308, the height

of the initial layer thickness in normal direction has been es-

timated for the SAGITTA demonstrator configuration to be

0.004 mm. With these input values, hybrid meshes have

been generated for both the tail-less demonstrator configu-

ration (”Clean”) and the configuration with attached vertical

tails (”VT Clean”). These meshes, whose approximate sizes

are summarized in Table 3, have been used for the numeri-

cal computations presented in this paper.

Surface Grid Prismatic Grid Hybrid Grid

Clean ≈ 360 ·103 ≈ 11.3 ·106 ≈ 14.5 ·106

VT Clean ≈ 517 ·103 ≈ 16.2 ·106 ≈ 20.7 ·106

Table 3: Approximate mesh size (number of elements) of

the considered configurations.


3

Furthermore, basic sketches of the generated surface

meshes are shown in Figure 3 and Figure 4. As example

for the tail-less configuration, the whole surface mesh is dis-

played, whereas for configuration VT Clean, only a detailed

view of the attached vertical tails is presented.

Figure 3: Surface mesh of the SAGITTA demonstrator con-

figuration without vertical tails.

Figure 4: Surface mesh of the attached vertical tails (con-

figuration VT Clean).

3.2 Flow Solver and Numerical Setup

The CFD computations conducted during the course of the

numerical investigations of the SAGITTA demonstrator con-

figuration have been performed with the DLR TAU-Code. It

solves the three-dimensional compressible Reynolds Aver-

aged Navier-Stokes (RANS) equations, is based on a finite

volume scheme and uses a dual-grid approach [12]. Fur-

thermore, it is developed to compute the RANS equations

on hybrid unstructured meshes in parallel mode.

In the present analysis, the one-equation turbulence

model by Spalart-Allmaras has been applied to the RANS

equations in its original version (SAO) [13]. For the finite

volume discretization, a second-order central scheme with

scalar dissipation has been used, while for the discretization

in time, an implicit Backward-Euler scheme with LUSGS al-

gorithm has been applied. The convergence of the com-

putations has been accelerated by a multigrid technique as

a 3v-cycle has been used. The computations have been

performed in parallel mode with up to 160 cores.

The CFD analyses presented in this paper have been

conducted for the cruise condition of the SAGITTA demon-

strator configuration carrying out steady-state computa-

tions. Designed for subsonic speeds of up to about

MaMax ≈ 0.35 and a ceiling height of hMax = 2500 m, the

cruise condition of the demonstrator UAV has been defined

to MaCruise = 0.3 and hCruise = 1000 m. Based on the mean

aerodynamic chord (MAC) of the diamond wing configura-

tion (noted in Table 1), the cruise Reynolds number results

in ReCruise = 12.7e6. The reference point for the moment

calculation has been set to the geometrical neutral point

of the wing at �X = [1.253,0,0] m behind the nose, which

almost coincides with the desired center of gravity of the

SAGITTA demonstrator. Thus, the computed moment coef-

ficients result in meaningful values for stability analyses.

The numerical investigations have been arranged further

for pure α- and β -polars at zero sideslip angle and zero

angle of attack, respectively. Thus, the range of computed

angles of attack at β = 0◦ reads α = [0◦;18◦], while the

lateral analyses are based on CFD results at α = 0◦ and

β = [0◦;14◦]. The maximum α- and β -values have thereby

been chosen with some safety margin due to relevant con-

straints within the flight envelope of the SAGITTA demon-

strator configuration (cross wind requirements and desired

landing speed). As a result of symmetry reasons of the

SAGITTA diamond wing, the computed force and moment

coefficients of the β -polar have additionally been mirrored

to negative sideslip angles for both demonstrator configu-

rations considered in this paper (Clean and VT Clean). In

contrast, the results of the α-polar have only been mirrored

to negative angles of attack for the tail-less configuration

(Clean), since the attached vertical tails break up the sym-

metry of the VT Clean configuration around the x-y plane.


4

4 WIND TUNNEL EXPERIMENTS

4.1 Wind Tunnel Facility and Model

The experimental analyses of the SAGITTA demonstrator

configuration have been performed in the wind tunnel facility

A of TUM-AER. The Gottingen-type low-speed wind tunnel

has an open test section with the dimensions (height x width

x length) of 1.8 m x 2.4 m x 4.8 m. The maximum velocity of

the open wind tunnel is U∞ = 65 m/s, but due to blockage

effects of the model, the maximum usable velocity can be

slightly lower.

For the wind tunnel tests, a 1:3-scaled model of the

SAGITTA demonstrator configuration has been built. The

resulting root chord length is cr,WT = 1 m, the wing span

reads bWT = 1.029 m and the wing reference area results in

SRe f ,WT = 0.528 m2. The model manufactured of fiber glass

is equipped not only with removable vertical tails, but also

with attachable landing gears; control surfaces for pitch, roll

and yaw control are also incorporated in the model, continu-

ously adjustable via model servos so that various flight ma-

neuvers can be measured. Rear mounted on the model’s

root section, the wind tunnel model has been held in the

test section by a sting support, Figure 5.

For measuring various angles of attack α and sideslip

angles β , a roll-yaw-mechanism of the sting support has

been used, which can be operated fully automatically. The

roll angle ϑ and the yaw angle ψ , which can be adjusted

computer-controlled, are mapped onto α and β by

α = arctan2(sinψ sinϑ ,cosψ) ∈ [−π;π](1)

β = arcsin(sinψ cosϑ) ∈[−π

2;

π2

].(2)

4.2 Force Measurements

The forces and moments acting on the wind tunnel model

have been measured by an external six-component strain

gauge balance located below the wind tunnel test section.

In order to correctly refer the moment components to the

geometrical neutral point of the wind tunnel model (de-

fined in concordance with the demonstrator configuration,

but scaled), the measured force and moment components

have been transformed automatically during data process-

ing from the strain gauge balance reference point to the

wind tunnel model reference point. Thus, the experimental

measured moments can easily be compared to the estab-

lished numerical data.

Figure 5: Wind tunnel model with sting support.

Due to a cover of the sting support, which has not been

connected at all to the sting itself, the force and moment

components acting on the sting cover have not been mea-

sured in the experiments by the strain gauge balance. Thus,

only static calibrations with the influence exerted by gravity

effects of the wind tunnel model are needed depending on

the desired α-β -combinations. Additional dynamic calibra-

tions have therefore been unnecessary. This method has

turned out to be very convenient for generating an aerody-

namic dataset with numerous data points to measure.

However, owing to practical reasons observed within the

wind tunnel experiments, the sting cover has not been con-

tinued exactly up to the trailing edge of the wind tunnel

model as intended at first, Figure 5. Thus, about 30cm of

the sting have not been protected by the sting cover and

have therewith contributed to the force and moment mea-

surements. This should be kept in mind for the further

analysis of the experimental data (see also Section 5.3), as

some effects of this experimental set-up must be expected

in the lateral degree of freedom.

4.3 Test Conditions, Measurement Ranges

and Considered Configurations

The force measurements of the SAGITTA demonstrator

wind tunnel model have been conducted at a velocity of

U∞ = 40 m/s at ambient pressure p∞ and ambient tem-

perature T∞, which have slightly varied between the experi-

ments. Based on the model’s MAC of lμ,WT = 0.667 m, the

Reynolds number of the wind tunnel tests is ReWT ≈ 1.7e6and the corresponding Mach number is MaWT ≈ 0.12.


5

According to predefined requirements within the SAGITTA

demonstrator program (see Section 3.2), the measurement

range of α-β -combinations has been set to angles of attack

of α = [−18◦;18◦] and sideslip angles of β = [−14◦;14◦].In contrast to the CFD computations, the experimental force

measurements have been performed for positive and nega-

tive angles of attack and sideslip angles, respectively.

Overall, force measurements have been arranged for

the tail-less configuration (Clean), the configuration with at-

tached vertical tails (VT Clean) and the landing configura-

tion with extended landing gears. In addition, each of the

control surfaces for roll, pitch and yaw control has been

tested thoroughly for different flap deflections. A total num-

ber of more than 7500 data points has been covered within

the wind tunnel experiments, which are to be used for

the aerodynamic data module (ADM). As initially discussed

above, only the results of the two different clean configu-

rations (Clean and VT Clean) are presented in this paper,

whereas the analysis of the control surfaces and the landing

configuration is not be regarded in the present publication.

5 RESULTS AND DISCUSSION

This section discusses and compares the results of the nu-

merical analyses and the experimental investigations of the

SAGITTA demonstrator configuration. At first, the defini-

tions of the aerodynamic force and moment coefficients are

introduced and briefly explained. Next, the longitudinal mo-

tion is regarded. Since the effect of the attached vertical

tails is not deemed to be considerable in this degree of free-

dom, only the tail-less clean configuration is considered. In

Section 5.3, the results of both configurations addressed

in this paper (Clean and VT Clean) are discussed, since

the vertical tails contribute most notably to the lateral mo-

tion of the SAGITTA demonstrator UAV. Hence, the effect of

attached vertical tails is evaluated by means of the compar-

ison of side force coefficients as well as rolling and yawing

moment coefficients.

Overall, the Reynolds similarity between numerics and

experiment is not valid in the present analysis as about one

order of magnitude lies between both Reynolds numbers

(ReWT /ReCFD ≈ 0.13). This fact is caused by the scaled

wind tunnel model and the maximum available test velocity

within the wind tunnel experiments. For the following pre-

sentation of the results, this aspect must be considered.

5.1 AERODYNAMIC FORCE AND MOMENT CO-

EFFICIENTS

In order to compare the aerodynamic force and moment co-

efficients to each other, the computed and measured body-

fixed forces and moments have been transformed to a wind-

fixed aerodynamic reference frame. Within this frame, the

x-axis points backwards in the direction of the freestream

velocity, while the y-axis points rightwards and the z-axis

upwards. The aerodynamic moments are defined in a right-

hand system, which corresponds to the positive axis direc-

tions as introduced above. Furthermore, the forces and mo-

ments have to be made dimensionless with appropriate ref-

erence quantities. Based on the aerodynamic forces lift (L),

drag (D) and side force (Y) as well as the aerodynamic mo-

ments rolling moment (l), pitching moment (m) and yawing

moment (n), the corresponding coefficients are defined with

the dynamic pressure q∞ as follows:

q∞ =12·ρ∞ ·U2

∞(3)

CD =D

q∞ ·SRe f(4)

CY =Y

q∞ ·SRe f(5)

CL =L

q∞ ·SRe f(6)

Cl =l

q∞ ·SRe f · s(7)

Cm =m

q∞ ·SRe f · lμ(8)

Cn =n

q∞ ·SRe f · s(9)

5.2 Longitudinal Motion

5.2.1 Drag Coefficient

The drag coefficient CD of the SAGITTA demonstrator clean

configuration is analyzed first. In Figure 6, the obtained CD-

values versus the angle of attack α for zero sideslip angle

β = 0◦ are shown. Both the numerical (CFD) and the ex-

perimental (WTT) data are illustrated. It is apparent that the

overall agreement between both data sets is quite good.

However, the drag coefficient curve corresponding to the

experimental values is slightly shifted to smaller CD-values

for small and moderate angles of attack in comparison to

the computed numerical data set. At α = 0◦, the values

of the zero drag coefficient CD,0 result in CD,0,WT = 0.0047and CD,0,CFD = 0.0071, respectively. Hence, the drag coef-


6

−20 −10 0 10 20 0

0.05

0.1

0.15

0.2

α [◦]

CD

[−]

CFD Clean - Beta=0◦WTT Clean - Beta=0◦

Figure 6: CD versus α - Clean Configuration.

ficient of the flying wing body is obviously underestimated in

the wind tunnel experiments. This can be explained by the

difference in the Reynolds numbers between the CFD com-

putations and the conducted wind tunnel measurements as

introduced above. While the CFD analyses have been com-

puted fully turbulent, the boundary layer of the wind tun-

nel model exhibits apparently some laminar regions with

smaller skin friction, which leads to the reduced drag co-

efficient values.

At high angles of attack (α = 16◦ and α = 18◦), the nu-

merical drag coefficient values are found to increase less

strongly than the experimental values, which show higher

drag coefficients in this region. At these α-values, separa-

tion effects at the diamond wing tips and vortex structures

in the inboard wing section become more and more dom-

inant, which also influences the convergence behaviour of

the CFD computations. In addition, unsteady effects play a

larger role, which have not been considered in the numer-

ics. Within the experiments, every data point has in contrast

been measured and averaged over 15 seconds. Hence,

one can expect larger differences in the force and moment

coefficients with increasing angles of attack.

As mentioned before in Section 3.2, the numerical data

set has been mirrored to negative angles of attack, whereas

the experimental data has been measured for negative α-

values as well. Comparing both the positive and the neg-

ative branches of the drag coefficient curves, it can be no-

ticed that the measured drag coefficient curve is not fully

symmetric around α = 0◦, contrary to the CFD data. At

negative angles of attack, slightly higher drag coefficients

are noticed. This observation indicates a small asymmetry

of the SAGITTA wind tunnel model with respect to the x-y

plane or rather small deficiencies in the correct positioning

of the wind tunnel model within the test section.

5.2.2 Lift Coefficient

Figure 7 plots the lift coefficient CL of the SAGITTA demon-

strator UAV versus the angle of attack α . In order to point

out some flow effects more clearly, Figure 7 also includes

illustrations of computed field streamlines around the dia-

mond wing configuration for different α-values.

� = 18°

� = 6°

� = 0°

� = 12°

Figure 7: CL versus α - Clean Configuration.

The overall characteristics of the lift coefficient curves are

described in a very similar way by both the CFD and the

WTT data. However, the lift coefficient curve observed ex-

perimentally for the positive α-branch slightly diverges from

the computed CL-α curve with increasing angles of attack,

whereas the agreement between the data sets for the neg-

ative α-branch is better. This observation can be more clar-

ified as the lift slope CL,α is displayed versus the angle of

attack, Figure 8. It can be clearly noticed that for moderate

angles of attack of up to about α ≤±8◦, the agreement be-

tween the CFD data and the WTT data is much better for

negative than for positive angles of attack. The global level


7

−20 −10 0 10 201.8

2

2.2

2.4

2.6

2.8

α [◦]

CL,α

[−]


Figure 8: CL,α versus α - Clean Configuration.

of the lift slope observed within the computations is about

CL,α ≈ 2.3, while the experimental lift slope results in about

CL,α ≈ 2.2 on the negative and about CL,α ≈ 2.05 on the

positive α-branch.

Considering the field streamlines in Figure 7, it can be

noticed that the vortices in the inboard wing section are al-

ready present at α = 6◦. At this angle of attack, however, no

dominant influence of the vortices on the lift characteristics

is observed, since the regions of low pressure at the vortex

core axes are not yet strongly developed. Thus, only a small

increase of the computed lift slope CL,α can be seen in Fig-

ure 8 for small angles of attack. This effect, not observed

for the experimental data, is mainly caused by the different

Reynolds numbers. Following, it can be assumed that the

formation of the vortex structures is Reynolds-dependent for

the present diamond wing UAV.

The decrease in the lift slope at angles of attack of α ≥ 8◦

and α ≥ 10◦, respectively, which can also be observed from

Figure 8, is caused by the evolving separations at the dia-

mond wing tip sections. As shown in Figure 7, the stream-

lines indicate no separation regions at the wing tips up to

α = 6◦. At an α-value of α = 12◦, in contrast, separation

regions are clearly noticeable at the diamond wing tips. Be-

ginning at α ≥ 8◦, these regions of separated flow increase

with increasing angle of attack, which leads to a decreased

lift slope CL,α . This effect is observed for both the CFD and

the WTT data. Moreover, up to an α-value of α ≤ 12◦ and

α ≤ 14◦, respectively, the effect of separation regions at

the wing tip sections is seen to be more powerful than the

lift-increasing effect of the inboard vortex systems.

If the angle of attack is even further increased, the lift

slope CL,α starts to increase again and continuously for the

CFD data. This observation is also explained by the influ-

ence of the vortex structures in the inboard wing section.

With increasing angle of attack, the leading-edge vortices

become more dominant and their effect on the lift charac-

teristics of the SAGITTA demonstrator UAV is now stronger

than the effect caused by the wing tip separations. High-

lighted by the streamlines for α = 12◦ and α = 18◦ in Fig-

ure 7, the vortex structures are clearly noticeable and more

distinctive than for α = 6◦. In addition, low pressure re-

gions are observed in the vicinity of the sharp trailing edge,

which are mainly responsible for the vortex generated lift

contribution. Because of several aspects concerning vortex

aerodynamics as introduced in Section 2 (non-slender di-

amond wing, 12 % relative airfoil thickness), however, the

non-linear lift contribution due to flow-dominating vortices

does not turn out to be very strong for the SAGITTA demon-

strator configuration. Considering once again the computed

lift coefficient curve in Figure 7, a pronounced non-linear

behaviour can not be recognized. If the angle of attack

would be increased even more, the non-linear lift contri-

bution would presumably increase and could be analyzed

more thoroughly.

Comparing the experimental lift coefficient data at nega-

tive and positive angles of attack around α ≥ ±12◦, a dif-

fusive behaviour is observed. In concordance with the CFD

data, the lift slope starts to increase again at α = 12◦, but

no continuous trend for negative and positive angles of at-

tack is noticed. The increase of CL,α is much more distinc-

tive than for the CFD data, but the trend is not continuous in

the positive α-branch. Corresponding to the observations

in the lift slope, small kinks are noticed for the experimental

data at high positive and negative angles of attack in Figure

7. In order to explain the different behaviour in comparison

to the CFD data, the Reynolds number dependence of the

vortex systems is stated again. For a more detailed expla-

nation, CFD data at a comparable Reynolds number would

be therefore of high interest. Moreover, possible interfer-

ence effects between the vortex systems and the sting be-

hind the model must be expected. Thus, the agreement of

the lift slope CL,α at high angles of attack between numerics

and the experiment is not as good as for small α-values.


8

5.2.3 Pitching Moment Coefficient

In order to conclude the longitudinal analysis of the

SAGITTA demonstrator clean configuration, the pitching

moment coefficient Cm is considered below. Figure 9

presents the results of both the numerics and the experi-

ment. As introduced in Section 3.2 and Section 4.2, the Cm-

values are referred to the geometrical neutral point of the

configuration, which is located at 41.6% of the root chord.

−20 −10 0 10 20−0.08

−0.04

0

0.04

0.08

α [◦]

Cm

[−]


Figure 9: Cm versus α - Clean Configuration.

Both the CFD and the WTT data show smaller Cm-values

with increasing angle of attack, which explains the negative

slope Cm,α of the curves observed. This indicates a sta-

ble behaviour of the SAGITTA demonstrator clean configu-

ration in the longitudinal degree of freedom. Furthermore,

the agreement between the CFD data and the WTT data

is once again more accurate at negative angles of attack.

This observation is directly associated with the findings pre-

sented in the previous subsection for the lift coefficient as

the pitching moment coefficient originates particularly from

the lift coefficient.

Since the clean configuration without attached vertical

tails is symmetric with respect to the x-y plane, a Cm,0-value

of Cm,0 = 0 at α = 0◦ is further expected. However, this is

only seen with the numerical results, whereas the wind tun-

nel experiment shows a small positive Cm,0-value. No ex-

act observation is found for this deficit in the experimental

values. In addition, the computed pitching moment coeffi-

cients exhibit by and large more linear characteristics than

the measured data set. With increasing absolute values of

the angle of attack, the slope of the Cm-curves increases,

but the increase is much more distinctive for the experimen-

tal values than for the CFD data. This effect is highlighted in

Figure 10, where the slope of the pitching moment curves,

the stability derivative Cm,α , is plotted versus the angle of at-

tack. It can be noticed that the difference of the Cm,α -values

is quite large at α = 0◦, but for higher positive and negative

α-values, the agreement becomes much better.

−20 −10 0 10 20−0.4

−0.3

−0.2

−0.1

0

α [◦]

Cm,α

[−]


Figure 10: Cm,α versus α - Clean Configuration.

5.3 Lateral Motion

5.3.1 Side Force Coefficient

The results concerning the lateral motion of the SAGITTA

demonstrator configuration are presented below. First of all,

the side force coefficient CY is analyzed for both configura-

tions considered in this paper (Clean and VT Clean). The

resulting values of numerics and experiment are shown in

Figure 11, which plots the coefficients versus the angle of

sideslip β at zero angle of attack. Regarding the tail-less

configuration (Clean), it can be seen that the flying-wing

body produces almost no side force with increasing angle

of sideslip, since the projected surface area that is exposed

to the cross wind flow is very small. In contrast to classical

wing-body configurations with a fuselage, for which the pro-

jected surface area drastically increases in cross wind flow,


9

−16 −8 0 8 16−0.04

−0.02

0

0.02

0.04

β [◦]

CY

[−]

CFD VT Clean - Alpha=0◦CFD Clean - Alpha=0◦WTT VT Clean - Alpha=0◦WTT Clean - Alpha=0◦

Figure 11: CY versus β - Clean & VT Clean Configuration.

the projected surface area of the SAGITTA diamond wing

is even reduced at non-zero sideslip angles. Thus, the re-

sults of the CFD data indicate CY -values close to zero for

all sideslip angles considered. In contrast, the experimen-

tal side force coefficients of the tail-less configuration show

small CY -values for non-zero angles of sideslip, which also

exhibit a relatively constant gradient over the β -sweep. This

effect is explained by the influence of the non-covered sting

part in the vicinity of the wing’s trailing edge, as mentioned

in Section 4.2. For measurements with a present angle of

sideslip, the non-covered sting part is slightly exposed to the

flow and contributes therewith to the force measurements

of the flying wing configuration. For future analyses with

the SAGITTA demonstrator wind tunnel model, this effect

should be eliminated when the sting cover is extended up

to the wind tunnel model.

If one compares the side force coefficients CY of the con-

figuration with attached vertical tails (Clean VT) to the afore-

mentioned tail-less configuration, the effect of the vertical

tails becomes obvious, Figure 11. The side force coeffi-

cients decrease for positive sideslip angles and increase for

negative β -values, respectively. Both the CFD and the WTT

data show a very good agreement for this configuration.

Moreover, the unwanted effect of the non-covered sting part

is no longer important, because the side force contribution

of the vertical tails dominate the side force coefficient CY in

its size.

In Figure 12, the derivative of CY with respect to the sideslip

angle β is shown. In this plot, the side force character-

istics can be analyzed more thoroughly. Comparing the

CFD data and the WTT data of configuration VT Clean, one

can again observe asymmetric effects on the positive and

the negative β -branch of the experimental data, which are

not present in the CFD data. As mentioned before, small

model asymmetries and a probable non-centric position-

ing within the wind tunnel test section have led to the ex-

perimental results presented in this publication. However,

manufacturing tolerances must always be considered and

can not completely be avoided, so pure symmetric data

sets are difficult to obtain. Overall, the global level of the

obtained CY,β -values varies over the sideslip angle β be-

tween CY,β ≈ −0.16 and CY,β ≈ −0.14 and fits quite good

to the computed CY,β -values. For the tail-less configuration

named Clean, the above mentioned non-zero gradient for

the experimental side force coefficient is furthermore no-

ticed, but the absolute value of the gradient is much smaller

than the CY,β -values of configuration VT clean.

−16 −8 0 8 16−0.18

−0.12

−0.06

0

0.06

β [◦]

CY,β

[−]


Figure 12: CY,β versus β - Clean & VT Clean Configuration.

5.3.2 Rolling Moment Coefficient

Subsequent to the presentation of the side force coefficient,

the rolling moment coefficient Cl is considered next. Figure

13 depicts the corresponding curves. Generally speaking,

for the tail-less configuration, the same aspects as for the


10

−16 −8 0 8 16−0.004

−0.002

0

0.002

0.004

β [◦]

Cl[−

]


Figure 13: Cl versus β - Clean & VT Clean Configuration.

side force coefficient appear in the resulting analysis. Due

to the symmetry of the flying wing body around the x-y plane

and the x-z plane, no rolling moment is observed within the

CFD data. As a result of small model deficiencies in the

wind tunnel model as argued in the previous sections, this

curve is not exactly reproduced by the experimental force

measurements, Figure 13. In fact, even the rolling moment

coefficient at β = 0◦ does not result in a Cl-value of Cl ≈ 0and hence, the curve seems to be slightly shifted up.

If the vertical tails are attached to the SAGITTA demon-

strator UAV, the symmetry around the x-y plane becomes

obsolete. For non-zero sideslip angles, a side force is gen-

erated at the vertical tails that acts with a lever arm around

the moment reference point located in the symmetry plane

of the diamond wing. Hence, the vertical tails generate a

non-zero rolling moment if a sideslip angle is present. The

comparison of numerics and experiment now agree quite

well, Figure 13. However, the experimental values once

again show asymmetric tendencies over the β -sweep, re-

sulting in a better agreement for the negative angles of

sideslip than for positive β -values. For the configuration

with attached vertical tails, the computed zero-rolling mo-

ment at β = 0◦ is also affirmed by the wind tunnel experi-

ment, as the rolling moment coefficient results at β = 0◦ in a

Cl-value of Cl = 0. Moreover, the corresponding derivative

Cl,β yields an averaged value of approximately Cl,β ≈ 0.06over the β -sweep for both the CFD and the WTT data.

If only the experimental results of both regarded configu-

rations are compared to each other, different signs in the

slope of the curves are noticed. While the rolling moment

coefficient curve of configuration VT Clean is confirmed by

the numerics and is expedient due to the effective force di-

rections acting on the vertical tails, the slope of the experi-

mental Cl-curve obtained for the tail-less configuration can

not be explained. In addition, the absolute difference in the

Cl-values of configuration Clean for β ± 14◦ is about 50%

of the maximum ΔCl of Configuration VT. For this result, no

explanation is found, since the generated side force coeffi-

cients of the tail-less diamond wing are considerably smaller

compared to configuration VT Clean, as presented in Sec-

tion 5.3.1. Thus, the effect of attached vertical tails should

be much more distinctive, which is however only shown by

the numerical results.

5.3.3 Yawing Moment Coefficient

Finally, the results obtained for the yawing moment coeffi-

cient Cn are presented below. Figure 14 illustrates the cor-

responding Cn-curves of the SAGITTA demonstrator UAV

for both regarded configurations (Clean and VT Clean) ver-

sus the angle of sideslip β .

−16 −8 0 8 16−0.04

−0.02

0

0.02

0.04

β [◦]

Cn[−

]


Figure 14: Cn versus β - Clean & VT Clean Configuration.

In contrast to the rolling moment coefficient, the yawing

moment coefficient Cn also becomes non-zero at present

sideslip angles for the tail-less demonstrator configuration,


11

which can clearly be observed by the numerical results of

configuration Clean. The associated slope of the curve that

is equivalent to the stability derivative Cn,β is found to be

slightly positive for the tail-less diamond wing. This effect is

caused by the chosen geometry planform of the SAGITTA

demonstrator UAV. Figure 15, in which the stability deriva-

tive Cn,β is plotted versus the sideslip angle β , is addition-

ally introduced for further discussion.

−16 −8 0 8 16−0.18

−0.12

−0.06

0

0.06

β [◦]

Cn,β

[−]


Figure 15: Cn,β versus β - Clean & VT Clean Configuration.

Within this figure, one can note the small positive Cn,β -

values of the CFD data for configuration Clean. Based on

the defined coordinate system as explained in Section 5.1,

a positive Cn,β -value indicates that the configuration is un-

stable in the lateral degree of freedom. Following, no weath-

ercock stability is achieved for pure lateral motion at α = 0◦

for the tail-less SAGITTA demonstrator configuration.

At this stage, the necessity of the attached vertical tails

becomes apparent, if the observed instability of configura-

tion Clean is not resolved by thrust-vectoring or the usage

of lateral control surfaces. Analyzing the results of config-

uration VT Clean in Figure 14 and Figure 15, the yawing

moment coefficients now result in significant higher values

with increasing sideslip angles and exhibit a negative slope.

Hence, the stability derivative Cn,β is also negative. The

attached vertical tails thus help the diamond wing config-

uration to become stable in the lateral degree of freedom

for zero angle of attack. For the first flight tests within

the SAGITTA demonstrator program, this weathercock sta-

bility is much appreciated. Therefore, the achieved Cn,β -

values of approximately Cn,β ≈−0.12 to Cn,β ≈−0.15 pro-

vide enough safety margin to operate the demonstrator UAV

safely in stable flight conditions.

At the very end, the characteristics of the yawing moment

coefficients are compared between the computed CFD data

and the measured WTT data. In concordance with the ob-

servations obtained for the other force and moment coef-

ficients, the agreement between numerics and experiment

is better for configuration VT Clean than for configuration

Clean. The aforementioned asymmetric effects within the

measured data are seen as well for the yawing moment

coefficients of both regarded configurations, but the over-

all agreement between CFD data and WTT data is quite

good. Furthermore, it is noticed that for configuration Clean

the negative β -branch is notably smoother, which is also

observed from the Cn,β -values in Figure 15.

6 CONCLUSION AND OUTLOOK

Both numerical and experimental studies have been investi-

gated on the SAGITTA diamond wing demonstrator configu-

ration to determine its aerodynamic characteristics. Two dif-

ferent configurations have been discussed in this paper, the

clean configuration consisting of just the flying wing body

(Clean) and the clean configuration with attached vertical

tails (VT Clean). For these configurations, numerically com-

puted force and moment coefficients have been compared

to experimentally measured values, which have been de-

rived from force measurements on a 1:3-scaled wind tunnel

model of the SAGITTA demonstrator UAV.

Overall, the results of the force and moment coefficients

discussed show a quite good agreement between the CFD

and the wind tunnel data. The most important trends of the

aerodynamic characteristics are reasonably predicted and

do not differ between the two different methods applied. The

experimental data sets, however, are found to exhibit some

asymmetric effects that should not be present as a result

of geometrical symmetries of the SAGITTA demonstrator.

These asymmetries are caused especially at higher angles

of attack by unsteady effects due to wing tip separation and

vortex systems in the inner wing section, whereas in general

also interference effects with the sting support and small

model deficiencies are made responsible for obtained dis-

crepancies, particularly in the lateral degree of freedom.


12

The necessity of vertical tails attached to the flying wing

body is pointed out by a stability analysis of both config-

urations considered for the yawing moment coefficient Cn.

Negative Cn,β -values, which indicate weathercock stability

in the defined coordinate system, are observed for present

sideslip angles at zero angle of attack only with attached

vertical tails. If no stabilizing vertical tails are attached, the

diamond wing UAV must be laterally stabilized by control

surfaces or a thrust-vectoring system.

Beyond the clean configurations of the SAGITTA demon-

strator UAV discussed in this publication, a lot more differ-

ent configurations have been tested in the wind tunnel ex-

periments, but are not further addressed in this paper. To-

gether with the aerodynamic coefficients obtained for de-

flected roll, pitch and yaw control devices as well as for the

landing configuration with extended landing gears, the aero-

dynamic characteristics of the SAGITTA demonstrator clean

configurations form the basis for the generation of the aero-

dynamic data module (ADM). This ADM contains all rele-

vant aerodynamic information about possible flight states of

the SAGITTA demonstrator within its flight envelope. For

the ADM, a very comprehensive data set has been created,

which is henceforward to be used within the SAGITTA re-

search program for further designing the demonstrator con-

figuration.

The generated experimental data set has additionally val-

idated the CFD computations for the clean configuration

with and without attached vertical tails presented in this

publication. Hence, the general validity of the numerical

analyses has hereby been confirmed. In order to compare

the results more thoroughly, new CFD data conducted at

a Reynolds number comparable to the wind tunnel exper-

iments would be of particular interest. In this case, ques-

tions concerning Reynolds number dependencies could be

analyzed in a much more detailed way.

Moreover, the understanding of the asymmetries ob-

tained within the experimental measurements should be in-

vestigated more intensively. For this analysis, further de-

tailed wind tunnel experiments would be necessary to study

the asymmetric effects discussed in this paper.

ACKNOWLEDGEMENTS

The support of this investigation by EADS CASSIDIAN

within the SAGITTA demonstrator program is gratefully ac-

knowledged. Moreover, the authors would like to thank the

SAGITTA partners for the fruitful and excellent co-operation.

The computer resources for the CFD computations pre-

sented in this publication have been provided by the Gauss

Center for Supercomputing/Leibnitz Supercomputing Cen-

ter (SuperMIG/SuperMUC) in Garching bei Munchen.

Furthermore, the authors thank the German Aerospace

Center (DLR) for providing the DLR TAU-Code used for the

numerical investigations carried out in this research project.

In addition, thanks goes to CENTAURSoft for its guidance

during the mesh generation process.

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